BLAS is just the library definition and not the implementation, so BLAS implementations could implement GEMM anyway they want. But in practice the triple loop m

BLAS is just the library definition and not the implementation, so BLAS implementations could implement GEMM anyway they want. But in practice the triple loop method (n^3) is the most common, despite Strassen's and the more numerically stable, Winograd methods being well known and available for decades. But with most things involving real computing hardware, memory access patterns and locality tend to be more important for performance than operation counts